Indexing metadata

Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs
 
2. Creator Author's name, affiliation, country Raphael Lachieze-Rey; Université Paris Descartes; France
 
2. Creator Author's name, affiliation, country Giovanni Peccati; Université de Luxembourg; Luxembourg
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Central Limit Theorems; Contractions; Malliavin Calculus; Poisson Limit Theorems; Poisson Space; Random Graphs; Stein's Method; $U$-statistics; Wasserstein Distance; Wiener Chaos
 
3. Subject Subject classification 60H07; 60F05; 60G55; 60D05
 
4. Description Abstract We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit theorems. These conditions can always be expressed in terms of contraction operators or, equivalently, fourth cumulants. Our findings are specifically tailored to deal with the normal approximation of the geometric $U$-statistics introduced by Reitzner and Schulte (2011). In particular, we shall provide a new analytic characterization of geometric random graphs whose edge-counting statistics exhibit asymptotic Gaussian fluctuations, and describe a new form of Poisson convergence for stationary random graphs with sparse connections. In a companion paper, the above analysis is extended to general $U$-statistics of marked point processes with possibly rescaled kernels.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-03-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2104
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2104
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.